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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Nonimmersion of lens spaces with 2-torsion


Author: A. J. Berrick
Journal: Trans. Amer. Math. Soc. 224 (1976), 399-405
MSC: Primary 57D40
MathSciNet review: 0420662
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Abstract: From a study of the equivariant unitary K-theory of the Stiefel manifold $ {V_{k + 1,2}}({\mathbf{C}})$, it is shown that the lens space $ {L^k}(n)$, with n a multiple of $ {2^{2k - 1 - \alpha (k - 1)}}$, does not immerse in Euclidean space of dimension $ 4k - 2\alpha (k) - 2$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0420662-3
Keywords: Complex G-vector bundle, complex Grassmannian, complex oriented Grassmannian, complex Stiefel manifold, equivariant unitary K-theory, immersion, lens space, projective tangent bundle
Article copyright: © Copyright 1976 American Mathematical Society